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- From Effective Strings to the Simplest theory of Quantum Gravity

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12100040

String-like objects arise in many quantum field theories.

Well known examples include flux tubes in QCD and cosmic strings. To a first approximation,

their dynamics is governed by the Nambu-Goto action, but for QCD flux tubes

numerical calculations of the energy levels of these objects have become so

accurate that a systematic understanding of corrections to this simple

description is desirable.

In the first part of my talk, I discuss an effective

field theory describing long relativistic strings. The construction parallels

that of the chiral Lagrangian in that it is based on the pattern of symmetry

breaking. To compare with previous works, I will present the results of the

calculation of the S-matrix describing the scattering of excitations on the

string worldsheet.

In the second part of my talk, I will discuss critical

strings from the same point of view and show that the worldsheet S-matrix in

this case is non-trivial but can be calculated exactly. I will show that it

encodes the familiar square-root formula for the energy levels of the string,

the Hagedorn behavior of strings, and argue that the theory on the string

worldsheet behaves like a 1+1 dimensional theory of quantum gravity rather than

a field theory.

If time permits, I will return to the task of computing

the energy levels of flux-tubes using lessons learned from the second part of

my talk.

©2012 Perimeter Institute for Theoretical Physics